Partial regularity for parabolic systems of double phase type
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909825434124288 |
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| author | Ok, Jihoon Scilla, Giovanni Stroffolini, Bianca |
| author_facet | Ok, Jihoon Scilla, Giovanni Stroffolini, Bianca |
| contents | We study partial regularity for nondegenerate parabolic systems of double phase type, where the growth function is given by $H(z,s)=s^p+a(z)s^q$, $z=(x,t)\inΩ_T$, with $\tfrac{2n}{n+2}<p\le q$ and $a(z)$ a nonnegative $C^{0,α,\fracα{2}}$-continuous function for some $α\in(0,1]$. As the main result we prove that if $q< \min \{p+\tfrac{αp }{n+2}, p+1 \}$ the spatial gradient of any weak solution is locally Hölder continuous, except on a set of measure zero. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_03849 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Partial regularity for parabolic systems of double phase type Ok, Jihoon Scilla, Giovanni Stroffolini, Bianca Analysis of PDEs 35D30, 35K55, 35K65 We study partial regularity for nondegenerate parabolic systems of double phase type, where the growth function is given by $H(z,s)=s^p+a(z)s^q$, $z=(x,t)\inΩ_T$, with $\tfrac{2n}{n+2}<p\le q$ and $a(z)$ a nonnegative $C^{0,α,\fracα{2}}$-continuous function for some $α\in(0,1]$. As the main result we prove that if $q< \min \{p+\tfrac{αp }{n+2}, p+1 \}$ the spatial gradient of any weak solution is locally Hölder continuous, except on a set of measure zero. |
| title | Partial regularity for parabolic systems of double phase type |
| topic | Analysis of PDEs 35D30, 35K55, 35K65 |
| url | https://arxiv.org/abs/2510.03849 |